基于时变Copula的伦铜和沪铜相关模式研究

Time-Varying Copula Research on the Dependence Patterns of the Futures Copper between LME and SHFE

基于时变Copula理论,构造了AR-GARCH-Time-varying-Joe-Clayton-Copula模型用于研究伦铜和沪铜的相关模式.先根据AIC信息准则,确定了AR和GARCH的阶,并基于分步极大似然估计计算得到AR-GARCH参数估计值;再用估计后AR-GARCH模型的残差进行概率累积变化,最后代入Time-varying-Joe-Clayton-Copula中得出时变参数.实证结果表明,前一天的伦铜对后一天的沪铜有着较强的影响,并且很好地描述了伦铜和沪铜的相关模式,充分反映了相关性信息.与常相关相比,时变相关更好地反应了市场的时变特性,表明伦铜和沪铜的相关性在尾部具有明显的时变性,而且下尾相关性略大于上尾.

Based on the Time-varying Copula, a modal, named AR-GARCH-Time- varying-Joe-Clayton-Copula, was constructed to research the dependence patterns of the Futures Coppers between LME and SHFE. Firstly, the order of AR and GRACH were fixed by AIC. Then, the parameters of AR-GARCH were estimated by using the step by step MLE. At last, by using the cumulative probability of transformation of residual in AR-GARCH, the parameters of Time-varying-Joe-Clayton-Copula were calculated by MLE. The empirical results showed that LME had strong influence on SHFE in the next day, and the model was able to characterize the dependence patterns be- tween LME and SHFE very well and described them thoroughly. Moreover, the time-varying model presented in our paper reflected the time varying character of the futures market better than the constant parameters copula. The model indicated that there existed visible time varying in the tail, and the dependence of low tail was larger than the upper tail.